Question

The number of ways of arranging letters of the word HAVANA so that V and N do not appear together is

Solution

Correct option is

80

 

We can arrange the letters H, A, A, A in  

                 

If one possible arrangement is  

              X X X X 

Then we can arrange V, N at any of the two places marked with O in the following arrangement. 

              O X O X O X O X O

This, we can arrange V and N in = 5P2 = 20 ways  

Thus, the number of ways in which letters can be arranged is

 4 × 20 = 80. 

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